Polycrystal Initial Conditions

Polycrystal Initial Conditions can be created in a few ways. They can be read from a file, generated with Voronoi Tesselation of a set of points, or placed in some regular crystal pattern such as hex or circles. In any case, it is advantageous to simulate such a system with a reduced number of order parameters for efficiency, which requires the use of the Grain Tracker. The trickiest part of running a reduced order parameter model however, is the initial assignment of order parameters to grains. This process is akin to solving a graph coloring. Fortunately, the order parameter assignment process has been taken care of for you. Each polycrystal initial condition should simply extend the PolycrystalUserObjectBase class.

Grain structure with associated neighbor graph overlaid.

Extentions of this class must begin by providing reporting the number of grains in the initial condition.

  virtual unsigned int getNumGrains() const = 0;
(modules/phase_field/include/userobjects/PolycrystalUserObjectBase.h)

Additionally, the developer must provide an implementation for reporting the grain(s) at every point in the domain:

  virtual void getGrainsBasedOnPoint(const Point & point,
                                     std::vector<unsigned int> & grains) const = 0;
(modules/phase_field/include/userobjects/PolycrystalUserObjectBase.h)

Finally, a method to report the variable value of the current order parameter at a point must be provided. This method is called after order parameters have been assigned to all grains.

  virtual Real getVariableValue(unsigned int op_index, const Point & p) const = 0;
(modules/phase_field/include/userobjects/PolycrystalUserObjectBase.h)

The object uses these implementations to build a grain adjacency graph that can be feed to a stochastic or deterministic graph coloring algorithm. MOOSE defaults to using one of the built-in high performance coloring algorithms from the PETSc package. However, a simple backtracking algorithm is also included which works reasonably well on smaller to mid-sized problems.

The centroids of grains can be randomly generated or read from a file. The use of Maximal Poisson-Disk Sampling (MPS) to generate grain centroids is described in MPS.

See:

PolycrystalVoronoi

PolycrystalEBSD

PolycrystalCircles

PolycrystalHex